Stata: Test difference in average RATE of two groups

Question: I need to test the difference in average (!) rates of two groups. Just to illustrate:
- Does the average rate of unemployed women in European countries differ from the average rate of unemployed women in US states
(so there is within-group (between countries and between states) variation and between group variation (between the US and Europe) - I'm interested only in the last.

"chitesti" by Cox seems to be a bit in the direction, but not what I need. Does anyone have a suggestion? I would be very grateful!!

It sounds like you have two independent sets of data, one of the unemployment rate for women in each European country [France, Germany, ...], and one for each US state [Alabama, Arkansas, ...]. You want to know if you can be confident that there is a difference between the means of each set. My text (Weiers) recommends an unequal-variances t-test, if you're comfortable with the assumption that the unemployment rates are normally distributed within each set. Excel can do this if you have the data analysis package installed, or probably any statistics program.

Thank you!!

Thank you very much!! After reading some texts myself, I came to this conclusion as well, using the "ttest Y, by(X) unequal level(95)" Stata command (and the Welch option - giving basically the same result).
Just checked your reply and was happy to have it confirmed
Indeed, equal variance assumption rejected.
Still thinking about if it is possible to do this with more categories (X-es) and whether things change with me using basically an entire (small, N=26) population.